The substitution-closure lwqo conjecture for permutation classes

Let $\mathcal{C}$ be a permutation class, and let $\langle\mathcal{C}\rangle$ denote its substitution closure. The substitution-closure conjecture. If $\langle\mathcal{C}\rangle$ is wqo, then $\mathcal{C}$, and hence also $\langle\mathcal{C}\rangle$, is lwqo. This is the substitution-closure analogue of the conjecture for one-point extensions and remains open.